%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO674-1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 02:28:36 PM UTC 2026
% Result : Unsatisfiable 3.15s 1.14s
% Output : Refutation 3.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 19
% Syntax : Number of formulae : 105 ( 9 unt; 5 def)
% Number of atoms : 575 ( 0 equ)
% Maximal formula atoms : 17 ( 5 avg)
% Number of connectives : 964 ( 494 ~; 465 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 8 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 9 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 173 ( 0 sgn 173 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ iLEQ(suc(X2),suc(X3))
| ~ 'E'(s('0'),f(X4))
| ~ 'E'(s('0'),f(suc(X5)))
| ~ 'E'(s('0'),f(suc(X4)))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(X3))
| ~ iLEQ(suc(X5),suc(X4))
| ~ iLEQ(suc(X4),suc(X2))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ iLEQ(suc(X1),suc(X0))
| ~ 'E'(s('0'),f(X5))
| ~ iLEQ(suc(X3),suc(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_193) ).
fof(f2,axiom,
! [X0] :
( ~ 'LE'(f(X0),s(s('0')))
| 'E'(s('0'),f(X0))
| 'LE'(f(X0),s('0')) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_298) ).
fof(f3,axiom,
! [X0] :
( iLEQ(suc(X0),suc(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_281) ).
fof(f4,axiom,
! [X0] :
( ~ 'LE'(f(X0),s('0'))
| 'E'('0',f(X0))
| 'LE'(f(X0),'0') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_176) ).
fof(f5,axiom,
! [X0] :
( ~ 'LE'(f(X0),s(s(s('0'))))
| 'E'(s(s('0')),f(X0))
| 'LE'(f(X0),s(s('0'))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_139) ).
fof(f6,axiom,
! [X0] :
( iLEQ(suc(X0),suc(X0))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_126) ).
fof(f7,axiom,
! [X0] : 'LE'(f(X0),s(s(s('0')))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_498) ).
fof(f8,axiom,
~ 'LE'(f(z),'0'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_204) ).
fof(f9,axiom,
! [X0] :
( ~ 'LE'(f(suc(X0)),s(s(s('0'))))
| 'E'(s(s('0')),f(suc(X0)))
| 'LE'(f(X0),s(s('0'))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_129) ).
fof(f10,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ 'E'(s(s('0')),f(suc(X5)))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X2))
| ~ iLEQ(suc(X3),suc(X4))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X5))
| ~ 'E'(s(s('0')),f(X1))
| ~ iLEQ(suc(X2),suc(X3))
| ~ 'E'(s(s('0')),f(suc(X4)))
| ~ 'E'(s(s('0')),f(suc(X3)))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(X3))
| ~ iLEQ(suc(X4),suc(X5))
| ~ 'E'(s(s('0')),f(X4))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ iLEQ(suc(X5),suc(X1))
| ~ iLEQ(suc(X0),suc(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_431) ).
fof(f11,axiom,
! [X0] :
( ~ 'LE'(f(suc(X0)),s('0'))
| 'E'('0',f(suc(X0)))
| 'LE'(f(X0),'0') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_50) ).
fof(f12,axiom,
! [X0] :
( ~ 'LE'(f(suc(X0)),s(s('0')))
| 'E'(s('0'),f(suc(X0)))
| 'LE'(f(X0),s('0')) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_84) ).
fof(f13,axiom,
! [X0] :
( iLEQ(suc(X0),suc(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_493) ).
fof(f14,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(X1))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X3),suc(X4))
| ~ 'E'('0',f(X5))
| ~ iLEQ(suc(X4),suc(X2))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(X3))
| ~ 'E'('0',f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X3))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(suc(X4)))
| ~ iLEQ(suc(X2),suc(X5))
| ~ 'E'('0',f(suc(X3)))
| ~ 'E'('0',f(suc(X5)))
| ~ 'E'('0',f(X4))
| ~ 'E'('0',f(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_453) ).
fof(f15,plain,
! [X0] :
( 'E'(s(s('0')),f(X0))
| 'LE'(f(X0),s(s('0'))) ),
inference(forward_subsumption_resolution,[],[f5,f7]) ).
fof(f16,plain,
! [X0] :
( 'E'(s(s('0')),f(suc(X0)))
| 'LE'(f(X0),s(s('0'))) ),
inference(forward_subsumption_resolution,[],[f9,f7]) ).
fof(f25,plain,
! [X2,X3,X0,X1,X4] :
( ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X1))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X3),suc(X4))
| ~ 'E'('0',f(X0))
| ~ iLEQ(suc(X4),suc(X0))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(X3))
| ~ 'E'('0',f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X3))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(suc(X4)))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'('0',f(suc(X3)))
| ~ 'E'('0',f(X4))
| ~ 'E'('0',f(X0)) ),
inference(factoring,[],[f14]) ).
fof(f27,plain,
! [X2,X3,X0,X1,X4] :
( ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X1))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X3),suc(X4))
| ~ 'E'('0',f(X0))
| ~ iLEQ(suc(X4),suc(X0))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(X3))
| ~ 'E'('0',f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X3))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(suc(X4)))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'('0',f(suc(X3)))
| ~ 'E'('0',f(X4)) ),
inference(duplicate_literal_removal,[],[f25]) ).
fof(f32,plain,
! [X2,X3,X0,X1,X4] :
( ~ 'E'('0',f(suc(X3)))
| ~ 'E'('0',f(X1))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X3),suc(X4))
| ~ 'E'('0',f(X0))
| ~ iLEQ(suc(X4),suc(X0))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(X3))
| ~ 'E'('0',f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X3))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(suc(X4)))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X4)) ),
inference(forward_subsumption_resolution,[],[f27,f3]) ).
fof(f39,plain,
! [X2,X3,X0,X1] :
( ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X1))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'('0',f(X3))
| ~ iLEQ(suc(X0),suc(X3))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X0))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(suc(X3)))
| ~ 'E'('0',f(X0)) ),
inference(factoring,[],[f32]) ).
fof(f43,plain,
! [X2,X3,X0,X1] :
( ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X1))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'('0',f(X3))
| ~ iLEQ(suc(X0),suc(X3))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X0))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(suc(X3))) ),
inference(duplicate_literal_removal,[],[f39]) ).
fof(f46,plain,
! [X2,X3,X0,X1] :
( ~ 'E'('0',f(suc(X3)))
| ~ 'E'('0',f(X1))
| ~ iLEQ(suc(X2),suc(X1))
| ~ 'E'('0',f(X3))
| ~ iLEQ(suc(X0),suc(X3))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X0))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(suc(X0))) ),
inference(forward_subsumption_resolution,[],[f43,f3]) ).
fof(f55,plain,
! [X2,X3,X0,X1,X4] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(X4))
| ~ 'E'(s('0'),f(X0))
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X2),suc(X0))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X4)))
| ~ iLEQ(suc(X1),suc(X4))
| ~ 'E'(s('0'),f(X3))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(factoring,[],[f1]) ).
fof(f59,plain,
! [X2,X3,X0,X1,X4] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(X4))
| ~ 'E'(s('0'),f(X0))
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X2),suc(X0))
| ~ 'E'(s('0'),f(suc(X4)))
| ~ iLEQ(suc(X1),suc(X4))
| ~ 'E'(s('0'),f(X3))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(duplicate_literal_removal,[],[f55]) ).
fof(f63,plain,
! [X2,X3,X0,X1,X4] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(X4))
| ~ 'E'(s('0'),f(X0))
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X2),suc(X0))
| ~ 'E'(s('0'),f(suc(X4)))
| ~ iLEQ(suc(X1),suc(X4))
| ~ 'E'(s('0'),f(X3))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(forward_subsumption_resolution,[],[f59,f13]) ).
fof(f70,plain,
! [X2,X0,X1] :
( ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X1))
| ~ iLEQ(suc(X2),suc(X1))
| ~ 'E'('0',f(X0))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X0))
| ~ 'E'('0',f(suc(X2))) ),
inference(factoring,[],[f46]) ).
fof(f71,plain,
! [X2,X0,X1] :
( ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X1))
| ~ iLEQ(suc(X2),suc(X1))
| ~ 'E'('0',f(X0))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X0))
| ~ 'E'('0',f(suc(X2))) ),
inference(duplicate_literal_removal,[],[f70]) ).
fof(f74,plain,
! [X2,X0,X1] :
( ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(X1))
| ~ iLEQ(suc(X2),suc(X1))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X0))
| ~ 'E'('0',f(suc(X0))) ),
inference(forward_subsumption_resolution,[],[f71,f3]) ).
fof(f81,plain,
! [X2,X3,X0,X1,X4] :
( ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X2))
| ~ iLEQ(suc(X3),suc(X0))
| ~ 'E'(s(s('0')),f(suc(X4)))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(X1))
| ~ iLEQ(suc(X2),suc(X3))
| ~ 'E'(s(s('0')),f(suc(X3)))
| ~ 'E'(s(s('0')),f(X4))
| ~ 'E'(s(s('0')),f(X3))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X4),suc(X2)) ),
inference(factoring,[],[f10]) ).
fof(f89,plain,
! [X2,X3,X0,X1,X4] :
( ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X2))
| ~ iLEQ(suc(X3),suc(X0))
| ~ 'E'(s(s('0')),f(suc(X4)))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(X1))
| ~ iLEQ(suc(X2),suc(X3))
| ~ 'E'(s(s('0')),f(suc(X3)))
| ~ 'E'(s(s('0')),f(X4))
| ~ 'E'(s(s('0')),f(X3))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X4),suc(X2)) ),
inference(duplicate_literal_removal,[],[f81]) ).
fof(f92,plain,
! [X2,X3,X0,X1,X4] :
( ~ 'E'(s(s('0')),f(suc(X2)))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X2))
| ~ iLEQ(suc(X3),suc(X0))
| ~ 'E'(s(s('0')),f(suc(X4)))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(X1))
| ~ iLEQ(suc(X2),suc(X3))
| ~ 'E'(s(s('0')),f(suc(X3)))
| ~ 'E'(s(s('0')),f(X4))
| ~ 'E'(s(s('0')),f(X3))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X4),suc(X2)) ),
inference(forward_subsumption_resolution,[],[f89,f6]) ).
fof(f97,plain,
! [X0,X1] :
( ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(X0))
| ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'('0',f(suc(X1))) ),
inference(factoring,[],[f74]) ).
fof(f100,plain,
! [X0,X1] :
( ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'('0',f(X1))
| ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'('0',f(suc(X1))) ),
inference(duplicate_literal_removal,[],[f97]) ).
fof(f101,plain,
! [X0,X1] :
( ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(X1))
| ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'('0',f(suc(X1))) ),
inference(forward_subsumption_resolution,[],[f100,f3]) ).
fof(f103,plain,
! [X0] :
( ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(X0))
| ~ iLEQ(suc(X0),suc(X0)) ),
inference(factoring,[],[f101]) ).
fof(f104,plain,
! [X0] :
( ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0))
| ~ iLEQ(suc(X0),suc(X0)) ),
inference(duplicate_literal_removal,[],[f103]) ).
fof(f105,plain,
! [X0] :
( ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0)) ),
inference(forward_subsumption_resolution,[],[f104,f3]) ).
fof(f109,plain,
! [X2,X3,X0,X1] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(X3))
| ~ 'E'(s('0'),f(X0))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ iLEQ(suc(X1),suc(X3))
| ~ 'E'(s('0'),f(X2))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(factoring,[],[f63]) ).
fof(f115,plain,
! [X2,X3,X0,X1] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(X3))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ iLEQ(suc(X1),suc(X3))
| ~ 'E'(s('0'),f(X2))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(duplicate_literal_removal,[],[f109]) ).
fof(f118,plain,
! [X2,X3,X0,X1] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(X3))
| ~ iLEQ(suc(X2),suc(X0))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ iLEQ(suc(X1),suc(X3))
| ~ 'E'(s('0'),f(X2))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(forward_subsumption_resolution,[],[f115,f13]) ).
fof(f141,plain,
! [X2,X3,X0,X1] :
( ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X0))
| ~ iLEQ(suc(X0),suc(X2))
| ~ 'E'(s(s('0')),f(suc(X3)))
| ~ 'E'(s(s('0')),f(X2))
| ~ 'E'(s(s('0')),f(X1))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'(s(s('0')),f(X3))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X3),suc(X0)) ),
inference(factoring,[],[f92]) ).
fof(f146,plain,
! [X2,X3,X0,X1] :
( ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X0))
| ~ iLEQ(suc(X0),suc(X2))
| ~ 'E'(s(s('0')),f(suc(X3)))
| ~ 'E'(s(s('0')),f(X2))
| ~ 'E'(s(s('0')),f(X1))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'(s(s('0')),f(X3))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X3),suc(X0)) ),
inference(duplicate_literal_removal,[],[f141]) ).
fof(f149,plain,
! [X2,X3,X0,X1] :
( ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X0))
| ~ iLEQ(suc(X0),suc(X2))
| ~ 'E'(s(s('0')),f(suc(X3)))
| ~ 'E'(s(s('0')),f(X2))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(X3))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X3),suc(X0)) ),
inference(forward_subsumption_resolution,[],[f146,f6]) ).
fof(f153,plain,
! [X2,X0,X1] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(X2))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ iLEQ(suc(X1),suc(X2))
| ~ 'E'(s('0'),f(X0))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(factoring,[],[f118]) ).
fof(f159,plain,
! [X2,X0,X1] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(X2))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(duplicate_literal_removal,[],[f153]) ).
fof(f161,plain,
! [X2,X0,X1] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(forward_subsumption_resolution,[],[f159,f13]) ).
fof(f163,plain,
! [X0,X1] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X0),suc(X0)) ),
inference(factoring,[],[f161]) ).
fof(f168,plain,
! [X0,X1] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X0),suc(X0)) ),
inference(duplicate_literal_removal,[],[f163]) ).
fof(f169,plain,
! [X0,X1] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(forward_subsumption_resolution,[],[f168,f13]) ).
fof(f171,plain,
! [X0] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(X0))
| ~ iLEQ(suc(X0),suc(X0)) ),
inference(factoring,[],[f169]) ).
fof(f172,plain,
! [X0] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0))
| ~ iLEQ(suc(X0),suc(X0)) ),
inference(duplicate_literal_removal,[],[f171]) ).
fof(f173,plain,
! [X0] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0)) ),
inference(forward_subsumption_resolution,[],[f172,f13]) ).
fof(f259,plain,
! [X2,X0,X1] :
( ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X0))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(X2))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X2),suc(X0)) ),
inference(factoring,[],[f149]) ).
fof(f260,plain,
! [X2,X0,X1] :
( ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X0))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(X2))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X2),suc(X0)) ),
inference(duplicate_literal_removal,[],[f259]) ).
fof(f263,plain,
! [X2,X0,X1] :
( ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(X2))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X2),suc(X0)) ),
inference(forward_subsumption_resolution,[],[f260,f6]) ).
fof(f269,plain,
! [X0,X1] :
( ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(X0))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X0),suc(X0)) ),
inference(factoring,[],[f263]) ).
fof(f272,plain,
! [X0,X1] :
( ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(X1))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X0),suc(X0)) ),
inference(duplicate_literal_removal,[],[f269]) ).
fof(f274,plain,
! [X0,X1] :
( ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(X1))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(forward_subsumption_resolution,[],[f272,f6]) ).
fof(f279,plain,
! [X0] :
( ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(X0))
| ~ iLEQ(suc(X0),suc(X0)) ),
inference(factoring,[],[f274]) ).
fof(f281,plain,
! [X0] :
( ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X0))
| ~ iLEQ(suc(X0),suc(X0)) ),
inference(duplicate_literal_removal,[],[f279]) ).
fof(f282,plain,
! [X0] :
( ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X0)) ),
inference(forward_subsumption_resolution,[],[f281,f6]) ).
fof(f284,plain,
! [X0] :
( ~ 'E'(s(s('0')),f(X0))
| 'LE'(f(X0),s(s('0'))) ),
inference(resolution,[],[f282,f16]) ).
fof(f286,plain,
! [X0] : 'LE'(f(X0),s(s('0'))),
inference(forward_subsumption_resolution,[],[f284,f15]) ).
fof(f287,plain,
! [X0] :
( 'LE'(f(X0),s('0'))
| 'E'(s('0'),f(X0)) ),
inference(resolution,[],[f286,f2]) ).
fof(f288,plain,
! [X0] :
( 'LE'(f(X0),s('0'))
| 'E'(s('0'),f(suc(X0))) ),
inference(resolution,[],[f286,f12]) ).
fof(f289,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'('0',f(X0))
| 'E'(s('0'),f(X0)) ),
inference(resolution,[],[f287,f4]) ).
fof(f290,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'('0',f(suc(X0)))
| 'E'(s('0'),f(suc(X0))) ),
inference(resolution,[],[f287,f11]) ).
fof(f291,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'('0',f(X0))
| 'E'(s('0'),f(suc(X0))) ),
inference(resolution,[],[f288,f4]) ).
fof(f292,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'('0',f(suc(X0)))
| 'E'(s('0'),f(suc(suc(X0)))) ),
inference(resolution,[],[f288,f11]) ).
fof(f293,plain,
( 'E'('0',f(z))
| 'E'(s('0'),f(z)) ),
inference(resolution,[],[f289,f8]) ).
fof(f295,definition,
( spl0_1
<=> 'E'(s('0'),f(z)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f299,definition,
( spl0_2
<=> 'E'('0',f(z)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f302,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f293,f299,f295]) ).
fof(f303,plain,
( 'E'('0',f(z))
| 'E'(s('0'),f(suc(z))) ),
inference(resolution,[],[f291,f8]) ).
fof(f304,plain,
( 'E'('0',f(suc(z)))
| 'E'(s('0'),f(suc(z))) ),
inference(resolution,[],[f290,f8]) ).
fof(f306,definition,
( spl0_3
<=> 'E'(s('0'),f(suc(z))) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f308,plain,
( 'E'(s('0'),f(suc(z)))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f310,definition,
( spl0_4
<=> 'E'('0',f(suc(z))) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f312,plain,
( 'E'('0',f(suc(z)))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f310]) ).
fof(f313,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f304,f310,f306]) ).
fof(f320,plain,
( ~ 'E'(s('0'),f(z))
| ~ spl0_3 ),
inference(resolution,[],[f308,f173]) ).
fof(f321,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f320,f306,f295]) ).
fof(f322,plain,
( 'E'('0',f(suc(z)))
| 'E'(s('0'),f(suc(suc(z)))) ),
inference(resolution,[],[f292,f8]) ).
fof(f324,definition,
( spl0_5
<=> 'E'(s('0'),f(suc(suc(z)))) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f326,plain,
( 'E'(s('0'),f(suc(suc(z))))
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f324]) ).
fof(f327,plain,
( spl0_5
| spl0_4 ),
inference(avatar_split_clause,[],[f322,f310,f324]) ).
fof(f328,plain,
( ~ 'E'('0',f(z))
| ~ spl0_4 ),
inference(resolution,[],[f312,f105]) ).
fof(f336,plain,
( spl0_3
| spl0_2 ),
inference(avatar_split_clause,[],[f303,f299,f306]) ).
fof(f337,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f328,f310,f299]) ).
fof(f351,plain,
( ~ 'E'(s('0'),f(suc(z)))
| ~ spl0_5 ),
inference(resolution,[],[f326,f173]) ).
fof(f352,plain,
( $false
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f351,f308]) ).
fof(f353,plain,
( ~ spl0_3
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f352]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f302]) ).
cnf(s2,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f313]) ).
cnf(s3,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(sat_conversion,[],[f321]) ).
cnf(s4,plain,
( spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f327]) ).
cnf(s6,plain,
( spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f336]) ).
cnf(s7,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(sat_conversion,[],[f337]) ).
cnf(s9,plain,
( ~ spl0_3
| ~ spl0_5 ),
inference(sat_conversion,[],[f353]) ).
cnf(s10,plain,
spl0_4,
inference(rat,[],[s9,s2,s4]) ).
cnf(s11,plain,
~ spl0_2,
inference(rat,[],[s7,s10]) ).
cnf(s12,plain,
spl0_3,
inference(rat,[],[s6,s11]) ).
cnf(s13,plain,
spl0_1,
inference(rat,[],[s1,s11]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s3,s12,s13]) ).
fof(f354,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO674-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n008.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 18:03:39 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running first-order theorem proving
% 0.09/0.24 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.15/1.14 % (2483782)Input is clausal, will run a generic CNF schedule.
% 3.15/1.14 % (2483787)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3632715845:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.15/1.14 % (2483792)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3292320028:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.15/1.14 % (2483791)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2914341041:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.15/1.14 % (2483789)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2965433074:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.15/1.14 % (2483790)lrs+10_1_sil=8000:sp=occurrence:random_seed=3496739892:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.15/1.14 % (2483788)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=303459120:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.15/1.14 % (2483793)dis-21_1_sil=8000:lcm=predicate:random_seed=3952357092:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.15/1.14 % (2483791)Refutation not found, incomplete strategy
% 3.15/1.14 % (2483791)------------------------------
% 3.15/1.14 % (2483791)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.15/1.14 % (2483790)Refutation not found, incomplete strategy
% 3.15/1.14 % (2483790)------------------------------
% 3.15/1.14 % (2483790)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.15/1.14 % (2483790)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.15/1.14 % (2483791)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.15/1.14 % (2483790)CaDiCaL version: 2.1.3
% 3.15/1.14 % (2483791)CaDiCaL version: 2.1.3
% 3.15/1.14 % (2483791)Termination reason: Refutation not found, incomplete strategy
% 3.15/1.14 % (2483791)Time elapsed: 0.001 s
% 3.15/1.14 % (2483790)Termination reason: Refutation not found, incomplete strategy
% 3.15/1.14 % (2483790)Time elapsed: 0.001 s
% 3.15/1.14 % (2483791)Peak memory usage: 86 MB
% 3.15/1.14 % (2483790)Peak memory usage: 86 MB
% 3.15/1.14 % (2483792)First to succeed.
% 3.15/1.14 % (2483792)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2483782"
% 3.15/1.14 % (2483793)Also succeeded, but the first one will report.
% 3.15/1.14 % (2483790)------------------------------
% 3.15/1.14 % (2483790)------------------------------
% 3.15/1.14 % (2483791)------------------------------
% 3.15/1.14 % (2483791)------------------------------
% 3.15/1.14 % (2483792)Refutation found. Thanks to Tanya!
% 3.15/1.14 % SZS status Unsatisfiable for theBenchmark
% 3.15/1.14 % SZS output start Proof for theBenchmark
% See solution above
% 3.77/1.25 % (2483792)------------------------------
% 3.77/1.25 % (2483792)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.77/1.25 % (2483792)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.25 % (2483792)CaDiCaL version: 2.1.3
% 3.77/1.25 % (2483792)Termination reason: Refutation
% 3.77/1.25 % (2483792)Time elapsed: 0.031 s
% 3.77/1.25 % (2483792)Peak memory usage: 89 MB
% 3.77/1.25 % (2483792)Instructions burned: 68 (million)
% 3.77/1.25 % (2483792)------------------------------
% 3.77/1.25 % (2483792)------------------------------
% 3.77/1.25 % (2483782)Success in time 0.456 s
% 3.77/1.25 % Vampire exiting
%------------------------------------------------------------------------------